scholarly journals Unfolding through processes to compute the complete prefix of Petri nets

2017 ◽  
Vol Volume 27 - 2017 - Special... ◽  
Author(s):  
Médésu Sogbohossou ◽  
Antoine Vianou
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Partial Order ◽  
Petri Net ◽  
The State ◽  
Classical Approach ◽  
New Approach ◽  
State Space Explosion ◽  
Single Process ◽  
Partial Order Semantics

The partial-order technique of the unfolding implicitly represents state-space of a Petri net (PN), by in particular preserving the concurrency relations between the events. That makes it possible to contain state-space explosion problem in case of strong concurrency. A complete prefix of unfolding is used to cover all the state-space of a bounded PN: its computation according to the classical approach is based on the concept of adequate order, taking directly into account only safe PN. In this paper, a new approach independent of the concept of adequate order and faithful to the partial-order semantics, consists in creating the events of the unfolding in the context of a single process at the same time. The results of the tests are conclusive for safe and nonsafe PN. Some solutions are presented to improve compactness of the prefix obtained. La technique d'ordre partiel du dépliage représente implicitement l'espace d'état d'un réseau de Petri (RdP), en conservant notamment les relations de concurrence entre les événements. Cela permet de contenir le phénomène de l'explosion combinatoire en cas de forte concurrence. Un préfixe complet de dépliage sert à couvrir tout l'espace d'état d'un RdP borné: son calcul suivant l'approche classique se base sur le concept d'ordre adéquat, ne prenant directement en compte que les RdP saufs. Dans cet article, une nouvelle approche indépendante du concept d'ordre adéquat et fidèle à la sémantique d'ordre partiel, consiste à créer les événements du dépliage dans le contexte d'un unique processus à la fois. Les résultats des tests sont concluants pour les RdP saufs et non saufs. Des solutions sont présentées pour améliorer la compacité du préfixe obtenu.

The Quantitative Assessment of Domino Effects Based on Stochastic Petri Nets

2008 ◽  
Vol 44-46 ◽  
pp. 537-544
Author(s):  
Shi Yi Bao ◽  
Jian Xin Zhu ◽  
Li J. Wang ◽  
Ning Jiang ◽  
Zeng Liang Gao
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Quantitative Assessment ◽  
Stochastic Petri Nets ◽  
Industrial Park ◽  
Domino Effect ◽  
State Space Explosion ◽  
Stochastic Petri Net ◽  
Chemical Industrial Park

The quantitative analysis of “domino” effects is one of the main aspects of hazard assessment in chemical industrial park. This paper demonstrates the application of heterogeneous stochastic Petri net modeling techniques to the quantitative assessment of the probabilities of domino effects of major accidents in chemical industrial park. First, five events are included in the domino effect models of major accidents: pool fire, explosion, boiling liquid expanding vapour explosion (BLEVE) giving rise to a fragment, jet fire and delayed explosion of a vapour cloud. Then, the domino effect models are converted into Generalized Stochastic Petri net (GSPN) in which the probability of the domino effect is calculated automatically. The Stochastic Petri nets’ models, which are state-space based ones, increase the modeling flexibility but create the state-space explosion problems. Finally, in order to alleviate the state-space explosion problems of GSPN models, this paper employs Stochastic Wellformed Net (SWN), a particular class of High-Level (colored) SPN. To conduct a case study on a chemical industrial park, the probability of domino effects of major accidents is calculated by using the GSPN model and SWN model in this paper.

Vulnerability, Uncertainty and Probability (VUP) Quantification of a Network of Interacting Satellites Using Stochastic Petri Nets (SPN)

2013 ◽  
Author(s):  
Atefeh Einafshar ◽  
Farrokh Sassani
Keyword(s):  
Markov Chain ◽  
Quantitative Analysis ◽  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Stochastic Petri Nets ◽  
Discrete State ◽  
New Approach ◽  
Stochastic Petri Net ◽  
Discrete State Space

A new approach to Vulnerability, Uncertainty and Probability (VUP) quantification procedure using Stochastic Petri Nets within a network of interacting satellites is presented. A Stochastic Petri Net based model is developed to quantify VUP in a network of interacting satellites. Three indicators are proposed to determine the VUP definitions in interacting network of satellites. The proposed VUP quantification scheme addresses a methodology which employs a Stochastic Petri Net for quantitative analysis of the behavior of the network. With the random variables associated with the Petri Net transitions, the dynamic behavior of the cooperating satellites in a SPN model can be mapped onto a time-continuous Markov chain with discrete state space. After generating a Markov Stochastic Petri Net model, the probability of a given condition in the network at a specified time can be computed and quantified as well as the vulnerability and uncertainty of the system using the identified indicators.

scholarly journals Modular State Space Analysis of Coloured Petri Nets

1997 ◽  
Vol 26 (524) ◽  
Author(s):  
Søren Christensen ◽  
Laure Petrucci
Keyword(s):  
Petri Nets ◽  
State Space ◽  
The State ◽  
Total System ◽  
Entire System ◽  
State Spaces ◽  
Space Analysis ◽  
State Space Analysis ◽  
Full State ◽  
Local Properties

<p>State Space Analysis is one of the most developed analysis methods for Petri Nets. The main problem of state space analysis is the size of the state spaces. Several ways to reduce it have been proposed but cannot yet handle industrial size systems.</p><p>Large models often consist of a set of modules. Local properties of each module can be checked separately, before checking the validity of the entire system. We want to avoid the construction of a single state space of the entire system.</p><p>When considering transition sharing, the behaviour of the total system can be capture by the state spaces of modules combined with a Synchronisation Graph. To verify that we do not lose information we show how the full state space can be conctructed.</p><p>We show how it is possible to determine usual Petri Nets properites, without unfolding to the ordinary state space.</p>

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